Player's aim lags a tick behind visual crosshair position

Whenever you move your camera, the actual functional crosshair location lags behind where it shows visually by 1/20th of a second. This applies to sword swinging, block breaking, and anything else that you click on to interact with. This is mostly what causes the perceived hit registration issues in PvP since 1.8.

Video demonstration: https://youtu.be/HTw87opulQg

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Code analysis by Marcono1234 in this comment.